Sturm Liouville problems. Degree theory.

23 Outubro 2017, 15:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

Lemma of Lasota-Opial (without proof)

Sturm-Liouville problems

16 Outubro 2017, 15:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

Theorem on the variation of \theta at the point b.

Differential inequalities. Sturm-Liouvile problems.

11 Outubro 2017, 14:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

A result on differential inequalities. 

Sturm-Liouville problems. Eigenvalues and eigenfunctions. Prufer's change of variables. Comparison theorem for theta. Existence of eigenvalues.

By request of the students there was no lesson, we will replace it in the near future

4 Outubro 2017, 14:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

No lesson

Continuability of solutions of Cauchy problems

27 Setembro 2017, 14:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

Definition of extendable solution and of maximal solution. 

Existence of maximal solution when uniqueness of solution of Cauchy problems is guaranteed.

Asymptotic behavior of solutions which are defined in a finite interval.

Global existence of solutions in the sub-linear case.

Global existence and uniqueness of Cauchy problems associated with linear systems.